This application claims priority of No. 105134924 filed in Taiwan R.O.C. on Oct. 28, 2016 under 35 USC 119, the entire content of which is hereby incorporated by reference.
Field of the Invention
The invention relates to a virtual image display device, and more particularly to an augmented reality type wearable field curvature virtual image display system.
Description of the Related Art
The virtual image projection is to image an image source into a virtual image with a projection distance and a magnification power through an optical system. When the light of the image source is incident to a refractive type or reflective type optical system to cause the light divergence, a virtual image is produced at a position where no actual convergence of light beams occurs. So, a screen cannot receive a real image. An observer can see the complete virtual image when an exit pupil surface of the virtual image system coincides with the observer's pupil. In this case, a distance between the ocular lens and the pupil is an eye relief.
The refractive type virtual image optical system is mostly adopted in the device, such as a magnifier, a microscope or a telescope. Because its use relates to the observation of the specific target, it is unnecessary to observe the external environment in front of the eye at the same time. Also, the wear demand of the human body needs not to be considered. So, the number, volumes and weights of the optical assemblies in front of the eye are not the main factors to be considered upon design.
In the reflective type virtual image optical system, a reflective device may be utilized to generate the turning between the position of the virtual image and the optical axis of the optical system. So, most of the elements of the optical system can be transferred from the positions right ahead the eye to other positions. For the wearable application, the center of gravity of the optical system may be nearer to the head to decrease the torque and achieve the objective of beauty at the same time. The reflective device itself may be manufactured to have partial reflection and partial transmission properties, so that the wearer can observe a virtual image from the image source through the reflected light, and observe the external environment from the transmitting light at the same time. Such the element is referred to as an image combiner when being applied to the reflective type virtual image optical system.
The reflective type virtual image optical systems may be classified into an on-axis type and an off-axis type. The frequently seen types of the on-axis optical systems are classified according to the type of the image combiner, wherein the waveguide (see U.S. Pat. Pub. No. 2007/0091445), the polarizing beam splitter (see U.S. Pat. No. 7,369,317) and the half mirror (see U.S. Pat. No. 5,822,127) are frequently seen. The design of the on-axis reflective type virtual image optical system is adopted such that the virtual image looks like being located right ahead the user. In the architecture of the polarizing beam splitter and the half mirror, a reflective flat surface tilted by 45° needs to be equipped in front of the human eye to function as one portion of the image combiner. Thus, the image combiner becomes somewhat thick, and the thickness is increased with the increase of the design value of the system field angle.
The off-axis type optical systems may be classified into a holographic optical element (see U.S. Pat. No. 5,305,124) and an ordinary optical element according to the type of the image combiner. The invention relates to a reflective type off-axis type virtual image display system adopting the ordinary optical element functioning as the image combiner.
FIG. 1A shows a reflective type off-axis type virtual image projection system 1000. The system is applicable to a projection lens set 100, and the optical lens set in front of an image source 101 functions as a first imaging group 103. A partial reflection and partial transmission lens having the concave surface curvature functions as a second imaging group 106 while functioning as the image combiner. Upon operation, the image source 101 images a real image 105 within a focal length of the second imaging group 106 through the first imaging group 103 so that the system 1000 generates a virtual image plane 108 and an exit pupil 110. The two groups are not coaxial, so that a sufficient large included angle is formed between the main light 113 incident to the center of the second imaging group 106 and the reflected main light 113′ reflected from the second imaging group 106, that the virtual image is disposed right ahead the observer, and that no interference is formed between the head tissue and the projection lens set when the virtual image is being observed.
It is assumed that the head mounted display device has the following specifications: (a) the virtual image frame having the aspect ratio of 16:9 and the diagonal length of 60 inches must be provided when the virtual image is distant from the observer by 2.5 meters, that is, the sagittal effective field angle needs to be equal to about 30°; (2) the virtual image needs to be located right ahead of the observer and rightly faces the observer; and (3) the optical system cannot shield the field of vision of the human eye 111 and also cannot interface with any tissue of the head. The above-mentioned three conditions are concurrently satisfied, the following conditions must be achieved: (1) an included angle of 15° must be formed between the reflected main light 113′ and each of the reflected main lights 114′ and 115′, generated when the second imaging group 106 reflects the main lights 114 and 115 coming from two sides of the real image 105, so that the observer can see the virtual image frame with the equal width on the left and right sides, and the sagittal effective viewing angle of 30° may be provided; (2) an optical axis 109 of the virtual image must be coaxial with an eye's optical axis 112 so that the virtual image frame rightly faces the observer, wherein the optical axis 109 of the virtual image is defined as a normal passing through the geometric center of the virtual image frame; (3) the included angle of at least 45° must be present between an optical axis 104 of the first imaging group of the projection lens set 100 and the eye's optical axis 112 at the eye relief of 25 mm, that is, the system 1000 must have the lateral projection of more than 45° so as to avoid the interference between the human body and the optical system; and (4) the eye's optical axis 112 must overlap with the reflected main light 113′ so that the center of the virtual image frame is disposed right ahead the human eye. In other words, the eye's optical axis 112 must be determined according to the reflected main light 113′.
The first condition may be achieved by controlling the ratio of the height of the real image 105 to the focal length of the second imaging group 106 as 2 tan(15°). In order to satisfy the third condition, rotation is made about the apex of the second imaging group 106 serving as a center until the optical axis 104 of the first imaging group and an optical axis 107 of the second imaging group form an included angle of 22.5° so that the main light 113 and the reflected main light 113′ form the included angle of 45°. The off-axis design causes different light paths on two sides of the virtual image to generate the keystone distortion of FIG. 1C. In addition, the optical axis 109 of the virtual image plane 108 formed in the system cannot be coaxial with the eye's optical axis 112 and does not satisfy the second condition. The frame keystone distortions caused by the second condition, which is not held, and the third condition, which is held, result from that the optical axis 109 of the virtual image and the reflected main light 113′ are not coaxial. In this case, it is possible to select an observation surface 116 functioning as the virtual image frame to improve the keystone distortion and solve the problem that the optical axis 109 of the virtual image and the eye's optical axis 112 are not coaxial. However, because the real imaging surface is the virtual image plane 108, the clarity of the observation surface 116 is deteriorated due to the factor of the requirement on the depth of field.
The keystone distortion of the virtual image is calculated as follows:
the sagittal field angle of the virtual image:
                              θ          FOV                =                  2          ⁢                                          ⁢                                    tan                              -                1                                      ⁡                          (                                                                    H                    horizontal                                    ·                                      M                                          image                      ⁢                      _                      ⁢                      real                                                                                        2                  ⁢                                                                          ⁢                                      f                    combiner                                                              )                                                          (                  Equation          ⁢                                          ⁢          1                )                where Hhorizontal≡the height of the image source in the sagittal direction;    Mimage_real≡the magnification power of the first group of the imaging system;    −fcombiner≡the equivalent focal length of the second imaging group;    the center magnification power of the virtual image:
                                          M            VC                    +                                    q              C                                      f              combiner                                +          1                ;                            (                  Equation          ⁢                                          ⁢          2                )                where qc≡the center image distance of the virtual image; and    the real image serving as the center object distance of the object:
                              p          C                =                                            q              C                                      M              VC                                .                                    (                  Equation          ⁢                                          ⁢          3                )            
In order to make the optical axis 109 of the virtual image and the main light 113 form the sagittal included angle, the optical axis 107 of the second imaging group needs to tilt on the sagittal plane to make the optical axis 107 of the second imaging group and the optical axis 104 of the first imaging group form an included angle θt therebetween. According to the light beam travelling direction:    the left-side object distance of the sagittal direction of the real image:
                              p          L                =                              p            C                    +                                                                                          H                    horizontal                                    ·                                      M                                          image                      ⁢                      _                      ⁢                      real                                                                      2                            ·              sin                        ⁢                                                  ⁢                          θ              t                                                          (                  Equation          ⁢                                          ⁢          4                )            the right-side object distance of the real image of the sagittal direction:
                              p          R                =                              p            C                    -                                                                                          H                    horizontal                                    ·                                      M                                          image                      ⁢                      _                      ⁢                      real                                                                      2                            ·              sin                        ⁢                                                  ⁢                          θ              t                                                          (                  Equation          ⁢                                          ⁢          5                )            According to the virtual image observing direction of the human eye:    the left-side magnification power of the sagittal direction of the virtual image:
                              M          VL                =                                            f              combiner                                                      f                combiner                            -                              p                L                                              =                                                    q                L                                            f                combiner                                      +            1                                              (                  Equation          ⁢                                          ⁢          6                )            where qL≡the left-side image distance of the virtual image,the right-side magnification power of the sagittal direction of the virtual image:
                              M          VR                =                                            f              combiner                                                      f                combiner                            -                              p                R                                              =                                                    q                R                                            f                combiner                                      +            1                                              (                  Equation          ⁢                                          ⁢          7                )            where qR≡the right-side image distance of the virtual image.According to (6)/(7) is obtained that the ratio of the left-side magnification power to the right-side magnification power of the virtual image is:
                              Ratio          MLR                =                                            f              combiner                        -                          p              R                                                          f              combiner                        -                          p              L                                                          (                  Equation          ⁢                                          ⁢          8                )            
It is assumed that:    the height of the image source 101 in the sagittal direction is 8 mm,    the first imaging group 103 has the magnification power of 1.1,    the effective field angle of the virtual image is 30°,    in order to turn the light path by 45°, the inclination angle θt of the second imaging group must be 22.5°, and    the center image distance of the virtual image is 45 mm.It is obtained from (Equation 1) that
      θ    FOV    =            30      °        =                            2          ⁢                                          ⁢                                    tan                              -                1                                      ⁡                          (                                                8                  ⁢                                                                          ⁢                  mm                  ×                  1.1                                                  2                  ⁢                                                                          ⁢                                      f                    combiner                                                              )                                      →                  f          combiner                    =              16.42        ⁢                                  ⁢                  mm          .                    It is obtained from (Equation 2) that
      M    VC    =                              45          ⁢                                          ⁢          mm                          16.42          ⁢                                          ⁢          mm                    +      1        =          3.74      .      It is obtained from (Equation 3) that
      p    C    =                    45        ⁢                                  ⁢        mm            3.74        =          12.03      ⁢                          ⁢              mm        .            It is obtained from (Equation 4) that
      p    L    =                    12.03        ⁢                                  ⁢        mm            +                                                  8              ⁢                                                          ⁢              mm              ×              1.1                        2                    ·          sin                ⁢                                  ⁢                  22.5          ∘                      =          13.71      ⁢                          ⁢              mm        .            It is obtained from (Equation 5) that
      p    R    =                    12.03        ⁢                                  ⁢        mm            -                                                  8              ⁢                                                          ⁢              mm              ×              1.1                        2                    ·          sin                ⁢                                  ⁢                  22.5          ∘                      =          10.35      ⁢                          ⁢              mm        .            It is obtained from (Equation 6) that
      M    VL    =                    16.42        ⁢                                  ⁢        mm                              16.42          ⁢                                          ⁢          mm                -                  13.71          ⁢                                          ⁢          mm                      =          6.07      .      It is obtained from (Equation 7) that
      M    VR    =                    16.42        ⁢                                  ⁢        mm                              16.42          ⁢                                          ⁢          mm                -                  10.35          ⁢                                          ⁢          mm                      =          2.70      .      It is obtained from (Equation 8) that
      Ratio    MLR    =                              f          combiner                -                  p          R                                      f          combiner                -                  p          L                      =                                        16.42            ⁢                                                  ⁢            mm                    -                      10.35            ⁢                                                  ⁢            mm                                                16.42            ⁢                                                  ⁢            mm                    -                      13.71            ⁢                                                  ⁢            mm                              ≅              2.24        .            
It is obtained, from the above-mentioned Equations, that the left-side image height is about 2.24 times of the right side image height in the virtual image, as shown in FIG. 1C. According to (Equation 8), it is obtained that the virtual image has no keystone distortion in the condition of θt=0 or fcombiner=∞. Because the off-axis type head wearable display device needs to avoid the interference with the head, θt≠0. In order to satisfy the magnification power of the virtual image, fcombiner≠∞. So, the keystone distortion of the frame caused by the implemented Equations is inevitably present in the conditions that the virtual image has the magnification power and that an included angle is formed between the second imaging group and the light path of the imaging system.
It is also possible to explain the problem that the optical axis 109 of the virtual image and the eye's optical axis 112 are not coaxial from the point of view of Scheimpflug principle. Scheimpflug principle describes that extensions of the objective plane, the image plane and the imaging system plane commonly intersect at one finite point when the objective plane is not parallel to the imaging system plane. As shown in FIG. 1B-1, the real image 105 caused by the first imaging group is the objective plane 105′ and the second imaging group plane is the imaging system plane 106-1, and the included angle between the optical axes thereof is 22.5°, so that the first imaging group and the main light passing through the center of the virtual image form the included angle of 45°. In this case, the extension surfaces of the objective plane 105′, the virtual image plane 108-1 and the imaging system plane 106-1 commonly intersect at the point P1.
Referring to FIGS. 1B-2 and 1B-3, the first imaging group 103, the objective plane 105′ are the same as those of FIG. 1B-1; the imaging system plane 106-1 is moved closer to the objective plane 105′ by 1.4 mm to generate the imaging system plane 106-2, the virtual image plane 108-2 and the optical axis 109-2 of the virtual image; and the imaging system plane 106-2 is further moved closer to the objective plane 105′ by 2.1 mm to generate the imaging system plane 106-3, the virtual image plane 108-3 and the optical axis 109-3 of the virtual image. Thus, FIGS. 1B-1, 1B-2 and 1B-3 show the variation condition when the center distance between the objective plane 105′ and the imaging system plane 106-1 gradually reduces from 10.8 mm to 7.3 mm, wherein the included angle between the optical axes of the two planes is kept unchanged. The system magnification power, the common intersection points P1, P2 and P3, the virtual image planes 108-1, 108-2 and 108-3 and the optical axes 109-1, 109-2 and 109-3 of the virtual image change with the change of the center distance. Observing FIGS. 1B-1, 1B-2 and 1B-3 can obtain that the included angles between the optical axes 109-1, 109-2 and 109-3 of the virtual image and the eye's optical axis 112 get smaller as the system magnification power gets smaller. On the contrary, the included angle between the two optical axes gets larger (i.e., the extent to which the wearer laterally observes the virtual image gets larger) as the system magnification power gets higher.
In order to solve the problem caused in the reflective type off-axis type virtual image projection system, a holographic optical element functioning as an image combiner has been proposed. For example, U.S. Pat. No. 3,940,204 discloses a holographic optical element functioning an as an image combiner, wherein the objective plane is inclined to the first imaging group. Also, U.S. Pat. No. 4,763,990 discloses a holographic optical element functioning as an image combiner, wherein the first imaging group is divided into at least two groups which are not coaxial. In addition, the holographic optical element is more sensitive to the wavelength variation. In order to process the color image, U.S. Pat. No. 5,305,124 adopts a three-layer holographic optical element to solve the band covering problem of the holographic optical element to achieve the full-color frame.
The system adopting the ordinary optical element functioning as an image combiner may also solve the problem caused by the reflective type off-axis type virtual image projection system. For example, U.S. Pat. No. 4,026,641 discloses a reflective surface adopting a toroidal surface functioning as an image combiner, wherein an object surface being a toroidal surface is needed to coordinate therewith. Also, U.S. Pat. No. 5,576,887 discloses a reflective surface using a toroidal surface functioning as an image combiner, wherein the objective plane is significantly inclined to and shifted from the first imaging group. Furthermore, U.S. Pat. No. 7,542,209 discloses a reflective surface using an elliptic surface functioning as an image combiner, wherein the first imaging group needs to have a wedged prism, the objective plane is inclined to and shifted from the first imaging group, and the first imaging group is divided into at least two groups, which are not coaxial.